Complex Analysis: what is a contour integral?

The first video on contour integration, part of the complex analysis lecture series. Here we introduce the concept of a contour and what it means to integrate in the complex plane.

Complex analysis lectures:

If you like the videos and would like to support the channel:

You can follow me on Instagram for write ups that come in handy for my videos:

My LinkedIn:

[TI]

Video was pretty good. To get a clear intuition on what exactly an integral in complex analysis mean I recommend the book "Visual complex analysis" by Tristan Needham combined with vector calculus chapter in "Feynman lectures in physics".

[AB-nuwe]

Didn't I watch this on your other site, focusing on Complex Analysis. I keep going crazy. Not that watching it again is a bad thing as doing so builds strong bones and teeth.

[quanle]

Hi there! I just wanted to say that your video on complex analysis is fantastic. I'm starting to learn it again on my own, and your video has been a tremendous help. Great work, and thank you so much!

[快來快]

Although my math is bad, I still watch most of your videos idk I probably enjoy watching someone solving hard problems

[youknowwhatlol]

thanks for the video!
i didn't understand your proof (since i am a beginner in advanced calculus and analysis)...i don't know these sums are and most importantly - WHY we have this inequality....intuitively, for me, it doesn't make sense. Could you guys (or the admin) please enlighten me on this? Thanks so much, in advance :)

[ikarienator]

That's a very nice introduction! Can you cover the branch cut next time? I think I have never really understood it.

[notsodope]

Ok but 1/z dz integral is not ln(z) here😢

[spiderjerusalem]

Did you use shakarchi's complex analysis 🤔

[giacomocervelli]

Why did you upload this here and not on the second channel? (Just out of curiosity)

[anupamamehra]

hi thanks for this... by the way are you a bachelor in mathematics or physics?

[tifng]

I have a question about double intégrals: when you have a double intégral from 0 to Infinity, and the integrand is f(x, y) dx dy. My question is when can you inverse dx and dy (like what are the conditions on f ?)

[mtl.wraith]

could you do a line integral next? i see them for one formula in my physics class but they were not explained at all

[fuckayo-tifj]

I noticed something in one or your videos. I forgot which one but it was using lobachevsky formula. You had the integral from 0 to inf of sin(x)sec(x)/x and used the Lobachevsky integral formula. Yet, sec(x) is indeed pi periodic but with alternating signs, but it is not continuous which makes the formula non valid. This integral is basically the integral from 0 to infinity of tan(x)/x. The limit as x —> inf doesn’t exist anyways.